Interpolation Multiscale Amplitude Sensitivity Permutation Lempel–Ziv Complexity and Its Application to Mechanical Fault Diagnosis

Lempel-Ziv complexity (LZC) and its improved versions, as powerful tools for measuring signal complexity, have been widely applied in the field of mechanical fault diagnosis. However, they only take into account the amplitude information of signals while neglecting the self-similarity of signal waveforms, which limits their accuracy. To address this limitation, amplitude sensitivity permutation Lempel-Ziv complexity (ASPLZC) is proposed to comprehensively and accurately measure signal complexity, which incorporates both the amplitude information of signals and the self-similarity of signal waveforms through the fusion weighting of euclidean distance and cosine similarity. Furthermore, interpolation multiscale ASPLZC (IMASPLZC), as a multiscale version of ASPLZC, is proposed, which effectively captures local mutations in mechanical fault signals through local Hermite interpolation, enabling accurate measurement of signal complexity at different scales. Three simulation experiments demonstrate that ASPLZC exhibits superior stability and sensitivity, while IMASPLZC has better separability. Meanwhile, three mechanical fault diagnosis experiments show that IMASPLZC consistently achieves a higher average recognition accuracy than the other six nonlinear dynamic methods, indicating its prominent performance in mechanical fault diagnosis.